R. M. Friedberg demonstrated the existence of a recursive functional that agrees with no Banach-Mazur functional on the class of recursive functions. In this paper Friedberg's result is generalized to both α-recursive functionals and weak α-recursive functionals for all admissible ordinals α such that $\lambda , where α * is the Σ 1 -projectum of α and λ is the Σ 2 -cofinality of α. The theorem is also established for the metarecursive case, α = ω 1 , where α * = λ = ω